The paper will be published in a volume for the proceedings of the 4th Italian-Japanese workshop on ``Geometric Properties for Parabolic and Elliptic PDE’s'', held in Palinuro in May 2015

Abstract:

We show that a class of Poincaré-Wirtinger inequalities on bounded convex sets can be obtained by means of the dynamical formulation of Optimal Transport. This is a consequence of a more general result valid for convex sets, possibly unbounded.